urgent, need suggestion

[tans]

if average of 5 numbers x,y,z,5,7 is 8 then how can it be taken as true that range of those numbers is '2 or more' ? can any body explain?

bcz, acc to me when average 8, then sum is 40. if sum 40, then sum of x,y,z is 40-5-7=28. then to make the range minimum, the numbers will have to be 28/3=9.33333. so the range is always more than 2. is there any other possibility that can make the range =2 ?

[tans]

this is a powerprep question.

[bigduke]

I cant see a way how the range could be exactly equal to 2

[tans]

will u plz explain? i m really worrying about my performance.

[serg14]

How does the whole problem sound like?

[sally82]

I think this a problem where you don't have to do any calculations. If it is given that the you have the numbers x,y,z,5, and 7, then you can directly infer that the range of these numbers has to be at least 2. (7 - 5 = 2) The range would be two if for example x = y = y = 6 (but this case would of course contradict with the assumption that the average is 8). So as the range is at least two (independent of x, y, and z and for ANY average), it also has to be true that the range is AT LEAST two.
Note, that the statement 'the range is at least two' does not imply that there is a case where it is actually two and the average is 8. The statement the range is at least two is also true if the smallest possible range for this problem would be 4 because 4 is larger than 2.

[sleek04]

I agree with Sally.

you don't need any paper for this question.
The range is difference between the smallest and the largest numbers from the set.
As you already said, 28 should be sum of the three numbers.
There could be cases:
x = 5, y = 5, z should be 18. the range is higher than 2.
(Over here, I'm assuming the least values for x and y to make the range minimum, but to satisfy the condition, you should have z as the largest value)
Case 2:
a= 7, y = 7, z = 10.
and so on
For any case , the range is a minimum value of 2 or more.
I took only integers and this would also satisfy for any decimal numbers too.
Thanks,

[tans]

thanx a lot to all